I donated milk to my local hospital & it had no impact on ds whatsoever. It still comes down to the supply & demand thing so the more you feed/pump the more milk you make.
I used to pump in the morning from the other breast when I fed ds & then in the evening again after I had put ds down.
I was given bottles by the midwives & froze the milk immediately ( you just add whatever you collect until the bottle is full & then start a new one). The midwife came & collected the frozen milk & brought me new empties to fill.
You have to have a blood test initially which covers you for 3 months donating which checks you for various diseases. If you take some meds you can't donate, also not drink more than 2 units of alcohol regularly & no more than 5 cups of caffeinated tea/coffee a day.
I was worried that I might not be able to express enough to make it worth their while ( the midwives in my area run the scheme in their free time). However, they reassured me that even an ounce a day is fine & actually I used to donate about 5 ounces a day. Premature babies may only take 5ml per feed so a little goes a long way!
In my experience the longer I did it the more I had to express. The only pain was the washing & sterilising of the pump, but that wasn't really a biggy.
You can only donate up until your baby is 6 months old as then your milk is really quite different from what a premature baby needs.
I'm glad I did it & it made me feel good to think that I might have helped some babies survive.